A Variational merging approach to the spatial description of environmental variables

Abstract

High resolution images of environmental variables are highly valuable sources of information in research and environmental management. Obtaining spatially continuous information from ground observations is challenging due to the wide variety of factors that affect classical interpolation methods. While geostatistical methods have produced noteworthy results, they generally rely on important assumptions and strongly depend on the availability of observed data. In turn, satellite‐based or model‐based gridded images generally represent the global spatial structure of environmental variables, but are subject to bias. With the objective of exploiting the benefits of both sources of information, we propose a new mathematical formulation to merge observed data with gridded images of environmental variables using partial differential equations in a variational setting. With a …